1)What can you say about the motion of a body if:

a. its displacement-time graph is a straight line inclined with the time axis
b. its velocity-time graph is a straight line inclined with the same axis.
c. its velocity- time graph is a parabola

A)The velocity is constant and it is equal to the slope.

B)The acceleration is constant and equal to the slope of the line.

C)The acceleration is time dependent and is still equal to the slope of the line.

2)What conclusions can be drawn if a velocity-time graph is parallel to the time axis?

The object is moving at a constant rate.

Those are all correct answers

1) a. If the displacement-time graph is a straight line inclined with the time axis, it indicates a constant velocity motion. This means that the object is moving with a constant speed in a straight line.

b. If the velocity-time graph is a straight line inclined with the same axis, it indicates a constant acceleration motion. This means that the object is experiencing a constant change in velocity over time.

c. If the velocity-time graph is a parabola, it indicates a motion with changing acceleration. The slope of the graph represents the acceleration, and since it is changing, the object's acceleration is also changing over time.

2) If a velocity-time graph is parallel to the time axis, it means that the object's velocity is constant. This suggests that the object is moving at a constant speed without any change in its velocity over time.

To determine the conclusions for the given questions, we need to understand how to interpret the displacement-time and velocity-time graphs.

a. For a displacement-time graph that is a straight line inclined with the time axis, the body is undergoing uniform motion. This means that the object is moving with a constant velocity or speed, since the displacement is proportional to the time. The slope of the line represents the velocity of the body.

b. If the velocity-time graph is a straight line inclined with the same axis, it indicates that the body is undergoing uniform acceleration. This means that the object's velocity is changing at a constant rate. The slope of the line represents the acceleration of the body.

c. When the velocity-time graph is a parabola, it indicates that the motion is non-uniform and the acceleration is not constant. In this case, the object experiences varying acceleration. The slope of the line still represents the acceleration at any given point.

Now, let's move on to the second question. If a velocity-time graph is parallel to the time axis, it means that the velocity is constant throughout the entire motion. The object is moving at a constant rate without any acceleration or deceleration.

By interpreting the graphs and understanding the relationships between displacement, velocity, and acceleration, we can draw conclusions about the motion of a body.